In time dependent scattering theory we know three important examples: the wave equation around an obstacle, the Schrodinger and the Dirac equation with a scattering potential. In this paper another example from time dependent linear transport theory is added and considered in full detail. First the linear Boltzmann operator in certain Banach spaces is rigorously defined, and then the existence of the Moller operators is proved by use of the theorem of Cook-Jauch-Kuroda, that is generalized to the case of a Banach space.